TITLE: Conformally flat manifold with zero scalar
QUESTION [10 upvotes]: I would like to ask the following : Is there any example of a compact conformally flat Riemannian manifold $(M^n,g)$ with $n\geq 4$ which is not flat and has zero scalar curvature?

REPLY [5 votes]: Responding to the OP's comments on the duplicate question, the example that was given in dimension $4$ can be easily generalized to higher dimensions:

If $(M,g_M)$ has constant sectional curvature $+1$ and $(N,g_N)$ has constant sectional curvature $-1$, then the product manifold $(M\times N,g_M\oplus g_N)$ is conformally flat. This is proved, e.g., in Besse's book "Einstein manifolds" (see Example 1.167, p. 61).
  Furthermore, this product manifold has vanishing scalar curvature if and only if $\dim M=\dim N$.